15.5 DAG NODE PROJECTION
The projection operation is a many-to-one function that maps several nodes of the DAG onto a single node in a reduced DAG, which we refer to as 
. Thus, several tasks in the DAG are mapped to a single task in DAG. The projection operation allows for a better task workload and control design by multiplexing several nodes in the DAG to a single node in the 
. We explained in Chapters 10 and 11 how to perform the projection operation using a projection matrix P. To obtain the projection matrix, we require to define a desired projection direction d. The vector d belongs to the null space of P. Since we are dealing with a 2-D DAG, matrix P is a row vector and d is a column vector.
A valid projection direction must satisfy the inequality
In the following sections, we will discuss design space explorations for the three values of s obtained in Eqs. 15.8–15.11.